Problem: Simplify the following expression: $\sqrt{3}-\sqrt{27}+\sqrt{75}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{3}-\sqrt{27}+\sqrt{75}$ $= \sqrt{3}-\sqrt{9 \cdot 3}+\sqrt{25 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{3}-\sqrt{9} \cdot \sqrt{3}+\sqrt{25} \cdot \sqrt{3}$ $= \sqrt{3}-3\sqrt{3}+5\sqrt{3}$ Finally, simplify by combining the terms. $= ( 1 - 3 + 5 )\sqrt{3} = 3\sqrt{3}$